
where \(M=M_I\times M_Q\) , \(p=1-\frac{1}{M_I}\) , \(q=1-\frac{1}{M_Q}\) ,
\(a=\sqrt{\frac{6}{(M_I^2-1)+(M_Q^2-1)\beta ^2}}\) , \(b=\beta a\)  and \(\beta =d_Q/d_I\)  is the quadrature-to-in-phase decision distance ratio with \(d_I\)  and \(d_Q\)  being
the in-phase and quadrature decision distance, respectively and \(Q(t)\)  is the Gaussian \(Q\) -function defined by
\( Q(t)=\frac{1}{\sqrt{2\pi }}\int _{t}^{\infty }\mbox{exp}(-\frac{x^2}{2})dx\) .
For the convenience of analysis, (REF ) can be rewritten using an alternate expression of 1-\(D\)  and 2-\(D\)  Gaussian \(Q\) -functions, \(Q_z(t,\phi )\)  defined as [1]}
\(Q_z(t,\theta )=\frac{1}{\pi }\int _{0}^{\theta }\exp \left(-\frac{t^2}{2\sin ^2\phi }\right)d\phi ,\qquad t\ge 0.\) 
